in many cases in networks, instead of using all 8 bits for data, we often utilize only 7 bits for data and one bit for ‘control’. specifically, this control bit is an even-parity bit to ensure that the number of bit ‘1’ in total 8 bits-long data is always even. assume a binary symmetric channel with bit error probability pe as in the lecture note. all bit errors are independent of another. sender a now transmits an 8-bit long packet (7 data bits one even-parity bit) onto this binary symmetric channel. the receiver b receives a packet and there are total three possibilities: case 1: no bit has been inverted (no error) so the receiver successfully receives the packet. case 2: some bits are inverted (error!) and the receiver can correctly ‘detect’ the error. case 3: some bits are inverted (error!) but the receiver mistakenly concludes that the packet is (or appears to be) error-free. find the probability of each of these three cases (5 points each). no need to find a closed form. just leave your expression as is. note that the sum of the probabilities of these 3 cases should be equal to one.